5.29/2.45	WORST_CASE(Omega(n^1), O(n^1))
5.29/2.45	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.29/2.45	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.29/2.45	
5.29/2.45	
5.29/2.45	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.29/2.45	
5.29/2.45	(0) CpxIntTrs
5.29/2.45	(1) Koat Proof [FINISHED, 324 ms]
5.29/2.45	(2) BOUNDS(1, n^1)
5.29/2.45	(3) Loat Proof [FINISHED, 722 ms]
5.29/2.45	(4) BOUNDS(n^1, INF)
5.29/2.45	
5.29/2.45	
5.29/2.45	----------------------------------------
5.29/2.45	
5.29/2.45	(0)
5.29/2.45	Obligation:
5.29/2.45	Complexity Int TRS consisting of the following rules:
5.29/2.45	eval_start_start(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb0_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_bb0_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_0(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_0(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_1(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_1(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_2(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_2(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_3(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_3(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_4(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_4(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_5(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_5(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_6(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_6(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb1_in(v_x, v_y, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	eval_start_bb1_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: v_n > v__0
5.29/2.45	eval_start_bb1_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: v_n <= v__0
5.29/2.45	eval_start_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb1_in(v__0, v__01 + 1, v_m, v_n, v_x, v_y)) :|: v_m > v__01
5.29/2.45	eval_start_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb1_in(v__0 + 1, v__01 + 1, v_m, v_n, v_x, v_y)) :|: v_m > v__01 && v_m <= v__01
5.29/2.45	eval_start_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb1_in(v__0, v__01, v_m, v_n, v_x, v_y)) :|: v_m <= v__01 && v_m > v__01
5.29/2.45	eval_start_bb2_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_bb1_in(v__0 + 1, v__01, v_m, v_n, v_x, v_y)) :|: v_m <= v__01
5.29/2.45	eval_start_bb3_in(v__0, v__01, v_m, v_n, v_x, v_y) -> Com_1(eval_start_stop(v__0, v__01, v_m, v_n, v_x, v_y)) :|: TRUE
5.29/2.45	
5.29/2.45	The start-symbols are:[eval_start_start_6]
5.29/2.45	
5.29/2.45	
5.29/2.45	----------------------------------------
5.29/2.45	
5.29/2.45	(1) Koat Proof (FINISHED)
5.29/2.45	YES(?, 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 14)
5.29/2.45	
5.29/2.45	
5.29/2.45	
5.29/2.45	Initial complexity problem:
5.29/2.45	
5.29/2.45	1:	T:
5.29/2.45	
5.29/2.45			(Comp: ?, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.45	
5.29/2.45			(Comp: ?, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.45	
5.29/2.45			(Comp: ?, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.45	
5.29/2.45			(Comp: ?, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Testing for reachability in the complexity graph removes the following transitions from problem 1:
5.29/2.46	
5.29/2.46		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46	We thus obtain the following problem:
5.29/2.46	
5.29/2.46	2:	T:
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.29/2.46	
5.29/2.46	3:	T:
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	A polynomial rank function with
5.29/2.46	
5.29/2.46		Pol(evalstartbb3in) = 1
5.29/2.46	
5.29/2.46		Pol(evalstartstop) = 0
5.29/2.46	
5.29/2.46		Pol(evalstartbb2in) = 2
5.29/2.46	
5.29/2.46		Pol(evalstartbb1in) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart6) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart5) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart4) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart3) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart2) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart1) = 2
5.29/2.46	
5.29/2.46		Pol(evalstart0) = 2
5.29/2.46	
5.29/2.46		Pol(evalstartbb0in) = 2
5.29/2.46	
5.29/2.46		Pol(evalstartstart) = 2
5.29/2.46	
5.29/2.46		Pol(koat_start) = 2
5.29/2.46	
5.29/2.46	orients all transitions weakly and the transitions
5.29/2.46	
5.29/2.46		evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46	strictly and produces the following problem:
5.29/2.46	
5.29/2.46	4:	T:
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	A polynomial rank function with
5.29/2.46	
5.29/2.46		Pol(evalstartbb3in) = -V_3 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstartstop) = -V_3 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstartbb2in) = -V_3 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstartbb1in) = -V_3 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart6) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart5) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart4) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart3) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart2) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart1) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstart0) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstartbb0in) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(evalstartstart) = -V_4 + V_6
5.29/2.46	
5.29/2.46		Pol(koat_start) = -V_4 + V_6
5.29/2.46	
5.29/2.46	orients all transitions weakly and the transition
5.29/2.46	
5.29/2.46		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46	strictly and produces the following problem:
5.29/2.46	
5.29/2.46	5:	T:
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)              evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)              evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: ar_3 + ar_5, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)              evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)              evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Applied AI with 'oct' on problem 5 to obtain the following invariants:
5.29/2.46	
5.29/2.46	  For symbol evalstartbb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
5.29/2.46	
5.29/2.46	  For symbol evalstartbb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
5.29/2.46	
5.29/2.46	  For symbol evalstartbb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	This yielded the following problem:
5.29/2.46	
5.29/2.46	6:	T:
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)              evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)              evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ar_3 + ar_5, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)              evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)              evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	A polynomial rank function with
5.29/2.46	
5.29/2.46		Pol(koat_start) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstartstart) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstartbb0in) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart0) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart1) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart2) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart3) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart4) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart5) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstart6) = -V_2 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstartbb1in) = -V_1 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstartbb2in) = -V_1 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstartbb3in) = -V_1 + V_5
5.29/2.46	
5.29/2.46		Pol(evalstartstop) = -V_1 + V_5
5.29/2.46	
5.29/2.46	orients all transitions weakly and the transition
5.29/2.46	
5.29/2.46		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46	strictly and produces the following problem:
5.29/2.46	
5.29/2.46	7:	T:
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)              evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ?, Cost: 1)              evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)              evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ar_3 + ar_5, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ar_1 + ar_4, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)              evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Repeatedly propagating knowledge in problem 7 produces the following problem:
5.29/2.46	
5.29/2.46	8:	T:
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 0)                                koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: 1, Cost: 1)                                evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
5.29/2.46	
5.29/2.46			(Comp: ar_1 + ar_4 + ar_3 + ar_5 + 1, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)                                evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
5.29/2.46	
5.29/2.46			(Comp: ar_3 + ar_5, Cost: 1)                      evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ]
5.29/2.46	
5.29/2.46			(Comp: ar_1 + ar_4, Cost: 1)                      evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
5.29/2.46	
5.29/2.46			(Comp: 2, Cost: 1)                                evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
5.29/2.46	
5.29/2.46		start location:	koat_start
5.29/2.46	
5.29/2.46		leaf cost:	0
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Complexity upper bound 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 14
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Time: 0.376 sec (SMT: 0.273 sec)
5.29/2.46	
5.29/2.46	
5.29/2.46	----------------------------------------
5.29/2.46	
5.29/2.46	(2)
5.29/2.46	BOUNDS(1, n^1)
5.29/2.46	
5.29/2.46	----------------------------------------
5.29/2.46	
5.29/2.46	(3) Loat Proof (FINISHED)
5.29/2.46	
5.29/2.46	
5.29/2.46	### Pre-processing the ITS problem ###
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Initial linear ITS problem
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.29/2.46	
5.29/2.46	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.29/2.46	
5.29/2.46	      2: evalstart0 -> evalstart1 : [], cost: 1
5.29/2.46	
5.29/2.46	      3: evalstart1 -> evalstart2 : [], cost: 1
5.29/2.46	
5.29/2.46	      4: evalstart2 -> evalstart3 : [], cost: 1
5.29/2.46	
5.29/2.46	      5: evalstart3 -> evalstart4 : [], cost: 1
5.29/2.46	
5.29/2.46	      6: evalstart4 -> evalstart5 : [], cost: 1
5.29/2.46	
5.29/2.46	      7: evalstart5 -> evalstart6 : [], cost: 1
5.29/2.46	
5.29/2.46	      8: evalstart6 -> evalstartbb1in : A'=B, C'=D, [], cost: 1
5.29/2.46	
5.29/2.46	      9: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1
5.29/2.46	
5.29/2.46	     10: evalstartbb1in -> evalstartbb3in : [ A>=E ], cost: 1
5.29/2.46	
5.29/2.46	     11: evalstartbb2in -> evalstartbb1in : C'=1+C, [ F>=1+C ], cost: 1
5.29/2.46	
5.29/2.46	     12: evalstartbb2in -> evalstartbb1in : A'=1+A, C'=1+C, [ F>=1+C && C>=F ], cost: 1
5.29/2.46	
5.29/2.46	     13: evalstartbb2in -> evalstartbb1in : [ C>=F && F>=1+C ], cost: 1
5.29/2.46	
5.29/2.46	     14: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=F ], cost: 1
5.29/2.46	
5.29/2.46	     15: evalstartbb3in -> evalstartstop : [], cost: 1
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Removed unreachable and leaf rules:
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.29/2.46	
5.29/2.46	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.29/2.46	
5.29/2.46	      2: evalstart0 -> evalstart1 : [], cost: 1
5.29/2.46	
5.29/2.46	      3: evalstart1 -> evalstart2 : [], cost: 1
5.29/2.46	
5.29/2.46	      4: evalstart2 -> evalstart3 : [], cost: 1
5.29/2.46	
5.29/2.46	      5: evalstart3 -> evalstart4 : [], cost: 1
5.29/2.46	
5.29/2.46	      6: evalstart4 -> evalstart5 : [], cost: 1
5.29/2.46	
5.29/2.46	      7: evalstart5 -> evalstart6 : [], cost: 1
5.29/2.46	
5.29/2.46	      8: evalstart6 -> evalstartbb1in : A'=B, C'=D, [], cost: 1
5.29/2.46	
5.29/2.46	      9: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1
5.29/2.46	
5.29/2.46	     11: evalstartbb2in -> evalstartbb1in : C'=1+C, [ F>=1+C ], cost: 1
5.29/2.46	
5.29/2.46	     12: evalstartbb2in -> evalstartbb1in : A'=1+A, C'=1+C, [ F>=1+C && C>=F ], cost: 1
5.29/2.46	
5.29/2.46	     13: evalstartbb2in -> evalstartbb1in : [ C>=F && F>=1+C ], cost: 1
5.29/2.46	
5.29/2.46	     14: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=F ], cost: 1
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Removed rules with unsatisfiable guard:
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.29/2.46	
5.29/2.46	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.29/2.46	
5.29/2.46	      2: evalstart0 -> evalstart1 : [], cost: 1
5.29/2.46	
5.29/2.46	      3: evalstart1 -> evalstart2 : [], cost: 1
5.29/2.46	
5.29/2.46	      4: evalstart2 -> evalstart3 : [], cost: 1
5.29/2.46	
5.29/2.46	      5: evalstart3 -> evalstart4 : [], cost: 1
5.29/2.46	
5.29/2.46	      6: evalstart4 -> evalstart5 : [], cost: 1
5.29/2.46	
5.29/2.46	      7: evalstart5 -> evalstart6 : [], cost: 1
5.29/2.46	
5.29/2.46	      8: evalstart6 -> evalstartbb1in : A'=B, C'=D, [], cost: 1
5.29/2.46	
5.29/2.46	      9: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1
5.29/2.46	
5.29/2.46	     11: evalstartbb2in -> evalstartbb1in : C'=1+C, [ F>=1+C ], cost: 1
5.29/2.46	
5.29/2.46	     14: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=F ], cost: 1
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	### Simplification by acceleration and chaining ###
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Eliminated locations (on linear paths):
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	     23: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 9
5.29/2.46	
5.29/2.46	      9: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1
5.29/2.46	
5.29/2.46	     11: evalstartbb2in -> evalstartbb1in : C'=1+C, [ F>=1+C ], cost: 1
5.29/2.46	
5.29/2.46	     14: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=F ], cost: 1
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Eliminated locations (on tree-shaped paths):
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	     23: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 9
5.29/2.46	
5.29/2.46	     24: evalstartbb1in -> evalstartbb1in : C'=1+C, [ E>=1+A && F>=1+C ], cost: 2
5.29/2.46	
5.29/2.46	     25: evalstartbb1in -> evalstartbb1in : A'=1+A, [ E>=1+A && C>=F ], cost: 2
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Accelerating simple loops of location 9.
5.29/2.46	
5.29/2.46	   Accelerating the following rules:
5.29/2.46	
5.29/2.46	     24: evalstartbb1in -> evalstartbb1in : C'=1+C, [ E>=1+A && F>=1+C ], cost: 2
5.29/2.46	
5.29/2.46	     25: evalstartbb1in -> evalstartbb1in : A'=1+A, [ E>=1+A && C>=F ], cost: 2
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	   Accelerated rule 24 with metering function F-C, yielding the new rule 26.
5.29/2.46	
5.29/2.46	   Accelerated rule 25 with metering function -A+E, yielding the new rule 27.
5.29/2.46	
5.29/2.46	   Removing the simple loops: 24 25.
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Accelerated all simple loops using metering functions (where possible):
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	     23: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 9
5.29/2.46	
5.29/2.46	     26: evalstartbb1in -> evalstartbb1in : C'=F, [ E>=1+A && F>=1+C ], cost: 2*F-2*C
5.29/2.46	
5.29/2.46	     27: evalstartbb1in -> evalstartbb1in : A'=E, [ E>=1+A && C>=F ], cost: -2*A+2*E
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Chained accelerated rules (with incoming rules):
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	     23: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 9
5.29/2.46	
5.29/2.46	     28: evalstartstart -> evalstartbb1in : A'=B, C'=F, [ E>=1+B && F>=1+D ], cost: 9+2*F-2*D
5.29/2.46	
5.29/2.46	     29: evalstartstart -> evalstartbb1in : A'=E, C'=D, [ E>=1+B && D>=F ], cost: 9+2*E-2*B
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Removed unreachable locations (and leaf rules with constant cost):
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	     28: evalstartstart -> evalstartbb1in : A'=B, C'=F, [ E>=1+B && F>=1+D ], cost: 9+2*F-2*D
5.29/2.46	
5.29/2.46	     29: evalstartstart -> evalstartbb1in : A'=E, C'=D, [ E>=1+B && D>=F ], cost: 9+2*E-2*B
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	### Computing asymptotic complexity ###
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Fully simplified ITS problem
5.29/2.46	
5.29/2.46	   Start location: evalstartstart
5.29/2.46	
5.29/2.46	     28: evalstartstart -> evalstartbb1in : A'=B, C'=F, [ E>=1+B && F>=1+D ], cost: 9+2*F-2*D
5.29/2.46	
5.29/2.46	     29: evalstartstart -> evalstartbb1in : A'=E, C'=D, [ E>=1+B && D>=F ], cost: 9+2*E-2*B
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Computing asymptotic complexity for rule 28
5.29/2.46	
5.29/2.46	   Solved the limit problem by the following transformations:
5.29/2.46	
5.29/2.46	      Created initial limit problem:
5.29/2.46	
5.29/2.46	      9+2*F-2*D (+), F-D (+/+!), E-B (+/+!) [not solved]
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	      removing all constraints (solved by SMT)
5.29/2.46	
5.29/2.46	      resulting limit problem: [solved]
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	      applying transformation rule (C) using substitution {F==0,D==-n,E==1,B==0}
5.29/2.46	
5.29/2.46	      resulting limit problem:
5.29/2.46	
5.29/2.46	      [solved]
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	   Solution:
5.29/2.46	
5.29/2.46	      F / 0
5.29/2.46	
5.29/2.46	      D / -n
5.29/2.46	
5.29/2.46	      E / 1
5.29/2.46	
5.29/2.46	      B / 0
5.29/2.46	
5.29/2.46	   Resulting cost 9+2*n has complexity: Poly(n^1)
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Found new complexity Poly(n^1).
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	Obtained the following overall complexity (w.r.t. the length of the input n):
5.29/2.46	
5.29/2.46	   Complexity:  Poly(n^1)
5.29/2.46	
5.29/2.46	   Cpx degree:  1
5.29/2.46	
5.29/2.46	   Solved cost: 9+2*n
5.29/2.46	
5.29/2.46	   Rule cost:   9+2*F-2*D
5.29/2.46	
5.29/2.46	   Rule guard:  [ E>=1+B && F>=1+D ]
5.29/2.46	
5.29/2.46	
5.29/2.46	
5.29/2.46	WORST_CASE(Omega(n^1),?)
5.29/2.46	
5.29/2.46	
5.29/2.46	----------------------------------------
5.29/2.46	
5.29/2.46	(4)
5.29/2.46	BOUNDS(n^1, INF)
5.29/2.48	EOF